Geodesic
Best approximations and widths of some classes of convolutions in $L_{2}$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 284-294 Cet article a éte moissonné depuis la source Math-Net.Ru

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We find tight upper bounds for the best approximations by trigonometric polynomials of certain classes of periodic functions representable as convolutions with structural characteristics defined by various modifications of m-th order moduli of continuity in the metric of $L_{2}$. We also find exact values for the $n$-widths of convolution classes given by such smoothness characteristics.
Keywords: best approximation, periodic function, trigonometric polynomial, modulus of continuity of $m$th order, $n$-widths. 
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K.Tukhliev. Best approximations and widths of some classes of convolutions in $L_{2}$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 284-294. http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a26/

[1] Abilov V.A., Abilova F.V., “Nekotorye voprosy priblizheniya $2\pi$-periodicheskikh funktsii summami Fure v prostranstve $L_{2}(2\pi)$”, Mat. zametki, 76:6 (2004), 803–811 | DOI | MR | Zbl

[2] Shabozov M.Sh., Yusupov G.A., “Tochnye konstanty v neravenstvakh tipa Dzheksona i tochnye znacheniya poperechnikov nekotorykh klassov funktsii v $L_{2}$”, Sib. mat. zhurn., 52:6 (2011), 1414–1427 | MR | Zbl

[3] Vakarchuk S.B., Zabutnaya V.I., “Neravenstva tipa Dzheksona–Stechkina dlya spetsialnykh modulei nepreryvnosti i poperechniki funktsionalnykh klassov v prostranstve $L_2$”, Mat. zametki, 92:4 (2012), 497–514 | DOI | MR | Zbl

[4] Ligun A.A., “Nekotorye neravenstva mezhdu nailuchshimi priblizheniyami i modulyami nepreryvnosti v prostranstve $L_{2}$”, Mat. zametki, 24:6 (1978), 785–792 | MR | Zbl

[5] Pinkus A., $n$-widths in approximation theory, Springer-Verlag, Berlin, 1985, 291 pp. | MR | Zbl

[6] Tikhomirov V.M., Nekotorye voprosy teorii priblizhenii, Izd-vo MGU, M., 1976, 325 pp. | MR

[7] Stechkin S.B., “O nailuchshem priblizhenii nekotorykh klassov periodicheskikh funktsii trigonometricheskimi polinomami”, Izv. AN SSSR. Ser. matematicheskaya, 20:5 (1956), 643–648 | Zbl

[8] Korneichuk N.P., Ligun A.A., Doronin V.G., Approksimatsiya s ogranicheniyami, Naukova dumka, Kiev, 1982, 252 pp. | MR